Summary: Efficient estimation approach provides a useful tool for semiparametric analysis of failure time data if the main interest is estimation of regression parameters [J. Huang, Ann. Stat. 24, No. 2, 540–568 (1996; Zbl 0859.62032); T. Martinussen and T. H. Scheike, Biometrika 89, No. 3, 649–658 (2002; Zbl 1036.62109)]. This paper discusses the application of this approach to regression analysis of bivariate current status data arising from the proportional odds model [S. Yang and R. L. Prentice, J. Am. Stat. Assoc. 94, No. 445, 125–136 (1999; Zbl 0997.62079); D. Rabinowitz et al., Biometrics 56, No. 2, 511–518 (2000; Zbl 1060.62657)]. Current status data arise if each study subject is observed only once and often occur in fields including demographical studies and tumorigenicity experiments. For the analysis, the copula model is assumed for the joint survival function of two related failure time variables which are supposed to follow the proportional odds model marginally. Simulation studies indicate that the estimates of regression parameters derived perform well in practical situations and the methodology is illustrated using a set of data from a tumorigenicity experiment.